License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2014.337
URN: urn:nbn:de:0030-drops-44694
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4469/
Go to the corresponding LIPIcs Volume Portal

Gawrychowski, Pawel ; Manea, Florin ; Nowotka, Dirk

Testing Generalised Freeness of Words

pdf-format:
27.pdf (0.7 MB)

Abstract

Pseudo-repetitions are a natural generalisation of the classical notion of repetitions in sequences: they are the repeated concatenation of a word and its encoding under a certain morphism or antimorphism (anti-/morphism, for short). We approach the problem of deciding efficiently, for a word w and a literal anti-/morphism f, whether w contains an instance of a given pattern involving a variable x and its image under f, i.e., f(x). Our results generalise both the problem of finding fixed repetitive structures (e.g., squares, cubes) inside a word and the problem of finding palindromic structures inside a word. For instance, we can detect efficiently a factor of the form xx^Rxxx^R, or any other pattern of such type. We also address the problem of testing efficiently, in the same setting, whether the word w contains an arbitrary pseudo-repetition of a given exponent.

BibTeX - Entry

@InProceedings{gawrychowski_et_al:LIPIcs:2014:4469,
  author =	{Pawel Gawrychowski and Florin Manea and Dirk Nowotka},
  title =	{{Testing Generalised Freeness of Words}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{337--349},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Ernst W. Mayr and Natacha Portier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4469},
  URN =		{urn:nbn:de:0030-drops-44694},
  doi =		{10.4230/LIPIcs.STACS.2014.337},
  annote =	{Keywords: Stringology, Pattern matching, Repetition, Pseudo-repetition}
}

Keywords: Stringology, Pattern matching, Repetition, Pseudo-repetition
Collection: 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)
Issue Date: 2014
Date of publication: 05.03.2014

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI